We report the development of highly chemically crosslinked, ultra low density (~0.015 g/cc) polyurethane shape memory foams synthesized from symmetrical, low molecular weight and branched hydroxyl monomers. Sharp single glass transitions (Tg) customizable in the functional range of 45-70 °C were achieved. Thermomechanical testing confirmed shape memory behavior with 97-98% shape recovery over repeated cycles, a glassy storage modulus of 200-300 kPa and recovery stresses of 5-15 kPa. Shape holding tests under constrained storage above the Tg showed stable shape memory. A high volume expansion of up to 70 times was seen on actuation of these foams from a fully compressed state. Low in-vitro cell activation induced by the foam compared to controls demonstrates low acute bio-reactivity. We believe these porous polymeric scaffolds constitute an important class of novel smart biomaterials with multiple potential applications.